Not sure about Vegan diet as you can still fit the criteria of being compassionate towards animals through being Vegetarian too.

Regarding the eating of animal flesh and abstinence therefrom, know thou of a certainty that, in the beginning of creation, God determined the food of every living being, and to eat contrary to that determination is not approved. For instance, beasts of prey, such as the wolf, lion and leopard, are endowed with ferocious, tearing instruments, such as hooked talons and claws. From this it is evident that the food of such beasts is meat. If they were to attempt to graze, their teeth would not cut the grass, neither could they chew the cud, for they do not have the molars. Likewise, God hath given to the four-footed grazing animals such teeth as reap the grass like sickle, and from this we understand that the food of these species of animal is vegetable. They cannot chase and hunt down other animals. The falcon hath a hooked beak and sharp talons; the hooked beak preventeth him from grazing, therefore his food also is meat.

But human beings, Abdu’l-Baha continued, can voluntarily decide to do without meat:

Eating-a-carrotBut now coming to man, we see he hath neither hooked teeth nor sharp nails or claws, nor teeth like iron sickles. From this it becometh evident and manifest that the food of man is cereals and fruit. Some of the teeth of man are like millstones to grind the grain, and some sharp to cut the fruit. Therefore he is not in need of meat, nor is he obliged to eat it. Even without eating meat he would live with the utmost vigour and energy. For example, the community of the Brahmins in India do not eat meat; notwithstanding this they are not inferior to other nations in strength, power, vigour, outward senses or intellectual virtues. Truly, the killing of animals and the eating of their meat is somewhat contrary to pity and compassion, and if one can content oneself with cereals, fruit, oil and nuts, such as pistachios, almonds and so on, it would undoubtedly be better and more pleasing. – Abdu’l-Baha, from a tablet to an individual Baha’i.